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Proving operator identities

  • Thread starter QuantumJG
  • Start date
  • #1
32
0
How would I go about showing:

[tex] \hat{A}^{\dagger} + \hat{B}^{\dagger} = \left( \hat{A} + \hat{B} \right) ^{\dagger}[/tex]
 

Answers and Replies

  • #2
169
0
You could start from the definition of the Hermitean adjoint,
[tex] \langle \psi | A^\dagger | \phi \rangle = \langle \phi | A | \psi \rangle^*[/tex] and use that the complex conjugation is linear,
[tex] (a+b)^* = a^* + b^*[/tex].
 

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